This invention relates generally to a method and system for controlling the flow of gas in a mass flow controller and more specifically to a method and system for generating a digital control signal with a fast response to set point step input in a digital mass flow controller.
A mass flow controller (MFC) is a closed loop device that sets, measures, and controls the flow of the mass of a process gas. Semiconductor applications have been and continue to be the driving force behind product development in mass flow controller technology. Nonetheless, mass flow control is useful in other industries such as the pharmaceutical industry and food industry.
A thermal mass flow controller is composed of a front half which includes a flow sensor and a back half which includes a control valve. The flow sensor is often composed of two resistance temperature sensors wound around a capillary tube. When gas flows through the sensor, heat is carried downstream and the temperature difference is proportional to the mass flow rate of the gas. The control valve receives a signal via electronics from the flow sensor to regulate gas flow. Solenoid activated valves are often used as control valves because of their simplicity, quick response, robustness and low cost.
Unfortunately, thermal flow sensors have a slow response time since thermal changes take place over a relatively long period of time. For instance, in FIG. 1, a graphical representation of an actual flow versus time is shown alongside a graphical representation of sensed flow versus time. The y-axis indicates flow rate while the x-axis indicates time.
The actual flow is represented as an approximation to a unit step function u(t) where the flow rate reaches a steady state value within a negligible amount of time. xcfx84 is denoted as the time constant it takes for the sensed flow to reach 63% of the actual flow. This may be as much as 1.7 seconds. It takes approximately 5xcfx84 to reach at least 99% of the actual flow. Unfortunately, the time delay needed to establish an accurate measurement of the actual flow from the sensed flow can introduce errors in the valve control. Information regarding the flow rate through the control valve is fed back to the control valve. Delay in accurate feedback of this information may contribute to undesirable errors in the flow of gas into a process chamber.
FIG. 2 represents a method used in the prior art to compensate for the time delay in the sensed flow as compared to the actual flow. The actual flow is a unit step function of magnitude fo. FIG. 2 shows a first derivative feedback control loop 10 where a flow sense signal 12 is input into both a first gain stage 14, with gain=1, and a differentiator stage 16. The output of the differentiator 16 is input into a second gain stage 18, with gain=xcfx84. The output of gain stage 14 and gain stage 18 are added to produce output 20 of first derivative feedback control loop 10.
This method approximates flow signal 12 as an exponential signal given by,
f(t)=fo(1xe2x88x92et/r), xe2x80x83xe2x80x83eqn. 1
where fo is the final steady state flow rate, t is the time and xcfx84 is the time constant associated with the flow sensor. The output 20 is given by,                     output        =                              f            ⁡                          (              t              )                                +                      τ            ⁢                                                            ⅆ                                      f                    ⁡                                          (                      t                      )                                                                                        ⅆ                  t                                            .                                                          eqn        .                  xe2x80x83                ⁢        2            
Inserting eqn. 1 into eqn. 2 yields
output=fou(t). xe2x80x83xe2x80x83eqn. 3
The output of first derivative feedback control system 10 is a step response of magnitude fo that is equal to the actual flow fo u(t). Therefore the actual flow is more closely approximated using first derivative feedback control system 10 than using just sensed flow signal 12.
The prior art method detailed in FIG. 2 has three disadvantages. The first disadvantage is that flow sensors typically do not exhibit linear behavior. Therefore, there is a certain amount of error innate in the flow sensor signal that is input into a control system.
The second disadvantage is that differentiator is typically an analog device. Hardware implementation of a differentiation device is difficult to realize in the analog domain and consequently these methods often use approximate differentiation implemented by linear circuits.
Lastly, first derivative feedback control systems fail to recognize that the flow of gas through the mass flow controller is really not a true first order exponential. Therefore, there is a certain amount of error innate to this type of system.
Ultimately, there is a need for a method that accurately calculates the actual gas flow within a mass flow controller. The method should reduce or eliminate the non-linearities of the flow sensor. This method should also more accurately approximate the flow sense signal which is not a true exponential signal.
The present invention provides a system and method for controlling gas flow within a digital mass flow controller that substantially eliminates or reduces disadvantages and problems associated with previously developed systems and methods for controlling gas flow within a digital mass flow controller.
The present invention provides a method that calculates a digitally enhanced flow rate signal that more accurately represents an actual flow rate through the digital mass flow controller. The digitally enhanced flow rate signal is calculated using a sensed flow rate signal output from a flow sensor, a scaled first derivative of the sensed flow rate signal, and a scaled second derivative of the sensed flow rate signal. A set-point signal is compared to the digitally enhanced flow rate signal to create a digital error signal. The digital error signal is provided to a digitally realized PI (proportional integral) controller. The PI controller generates a digital control signal that is used to control a valve in the digital mass flow controller.
One advantage of the present invention is that the use of a second derivative enables a more accurate approximation of the sensor signal than the use of a first derivative alone. A more accurate approximation of the sensor flow rate signal enables a more precise and responsive control of the gas flow in a process.
Another advantage of the present invention is that the use of digital signals readily enables interfacing with digital processors such as computers. High speed digital processors can be accessed to aid in rigorous computations, during calibration for example, which may be too lengthy for any on-board DSP controller in the mass flow controller.